Have you wrapped your javascript in closures? http://doc.silverstripe.org/sapphire/en/topics/javascript#custom-jquery-code. Normally that prevents most conflict errors.

Actually I am using one script, that when wrapped, still has a conflict with the SiteNavigator.

I am using this plugin: http://sorgalla.com/jcarousel/

And the script in my header looks something like this:
<script type="text/javascript">
      (function($) {
       $(document).ready(function(){
       jQuery('#mycarousel01').jcarousel({
       // Configuration goes here
       });
         jQuery('#mycarousel02').jcarousel({
       // Configuration goes here
       });
         jQuery('#mycarousel03').jcarousel({
       // Configuration goes here
       });
         jQuery('#mycarousel04').jcarousel({
       // Configuration goes here
       });
         jQuery('#mycarousel05').jcarousel({
       // Configuration goes here
       });
         jQuery('#mycarousel06').jcarousel({
       // Configuration goes here
       });
      })
      })(jQuery);
      </script>

It works fine when the SiteNavigator isn't present but displays as a list (as opposed to a slider) when you're logged into the admin.

Any suggestions would be great. Thanks!